Mathematical models of flow of incompressible fluids

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Department of Mathematics

Synopsis:

The aim of the subject is to derive mathematical models of steady and nonsteady flow of incompressible fluids. Course contents: Vector and tenzor calculus, function spaces (Lebesque and Sobolev spaces), some known theorems of integral calculus that will be applied to derive mathematical models (Green's theorem, Stokes theorem, Gauss-Ostrograph's theorem), continuum and its kinematics, tenzor of small deformations, tenzor of velocity of deformation, Eulerian and Lagrangian description of motion, Reynolds transport theorem, the volume forces, the surface forces, the stress tenzor and its properties, constitutive equations, Stokesian fluids, basic types of Stokesian fluids: ideal fluid, Newtonian fluid, the pressure, the dynamic stress tensor, mathematical models of flow of incompressible fluid, formulation of boundary value problems for steady and nonsteady flow of incompressible fluid.

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